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PHYSICS, M4 EQ-Bank 7 MC

Consider the circuit below.
 

The readings on the meters are \(I_1\), \(I_2\), \(V_1\) and \(V_2\). Which of the following pairs of inequalities are correct.

  1. \(I_1 > I_2\) and \(V_1 > V_2\)
  2. \(I_1 > I_2\) and \(V_1 < V_2\)
  3. \(I_1 < I_2\) and \(V_1 > V_2\)
  4. \(I_1 < I_2\) and \(V_1 < V_2\)
Show Answers Only

\(A\)

Show Worked Solution
  • Let the supplied voltage to the circuit be 25 V.
  • The total resistance of the 4 \(\Omega\) and 8 \(\Omega\) resistors are:
\(\dfrac{1}{R_{T_1}}\) \(= \dfrac{1}{8} + \dfrac{1}{4} = \dfrac{3}{8}\)  
\(R_{T_1}\) \(=\dfrac{8}{3}\ \Omega\)  
  •  Similarly, the total resistance of the 3 \(\Omega\) and 3 \(\Omega\) resistors are:
\(\dfrac{1}{R_{T_2}}\) \(= \dfrac{1}{3} + \dfrac{1}{3} = \dfrac{2}{3}\)
\(R_{T_2}\) \(=\dfrac{3}{2}\ \Omega\)
  •  The total resistance of the circuit is \(\dfrac{8}{3} + \dfrac{3}{2} = \dfrac{25}{6}\ \Omega\)
  • The total current running through circuit is:
  •    \(I = \dfrac{V}{R} = \dfrac{25}{\frac{25}{6}} = 6\ \text{A}\)
  • The voltage drop across the first two resistors \(=R_{T_1} \times I = \dfrac{8}{3} \times 6 = 16\ \text{V}\)
  • Therefore the voltage drop across the second two resistors \(=25-16 = 9\ \text{V}\)
  • As the voltage across each branch of a parallel circuit is the same and equal to the total voltage drop, \(V_1 > V_2\)
  • The current in each branch of a parallel circuit is split depending on the resistance of each branch. 
  •    \(I_1 = \dfrac{V}{R} = \dfrac{16}{4} = 4\ \text{A}\)
  •    \(I_2 = \dfrac{V}{R} = \dfrac{9}{3} = 3\ \text{A}\)

\(\therefore I_1 > I_2\)

\(\Rightarrow A\)

PHYSICS, M4 EQ-Bank 4 MC

Which instrument is connected in series in an electric circuit, and why?

  1. Voltmeters, because they are designed to measure current through a component.
  2. Ammeters, because they must measure voltage drop across a component.
  3. Voltmeters, because they have very low resistance and should allow maximum current flow.
  4. Ammeters, because they have very low resistance and should not alter the current.
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\(D\)

Show Worked Solution
  • Ammeters are used to measure the current flowing through a circuit, and to do this accurately, they must be connected in series with the component whose current is being measured.
  • When connected in series, all the current flowing through the circuit also flows through the ammeter. To avoid affecting the current, ammeters are designed with very low internal resistance.
  • If they had high resistance, they would reduce the current in the circuit, giving incorrect readings and possibly interfering with the circuit’s operation.

\(\Rightarrow D\)